Dirceu Bagio

Partial Groupoid Actions: Globalization, Morita Theory, and Galois Theory

In this article, we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action, and we introduce the notion of a partial Galois extension, which is related to the strictness of this context.

Crossed Products by Twisted Partial Actions: Separability, Semisimplicity, and Frobenius Properties

In this article, we are concerned with the crossed product S = R☆α G by a twisted partial action α of a group G on a ring R. We give necessary and sufficient (resp., sufficient) conditions for S to be a separable (resp., Frobenius, semisimple) extension of R.

PARTIAL ACTIONS OF ORDERED GROUPOIDS ON RINGS

In this paper, we introduce the notion of a partial action of an ordered groupoid on a ring and we construct the corresponding partial skew groupoid ring. We present sufficient conditions under which the partial skew groupoid ring is either associative or unital. Also, we show that there is a one-to-one correspondence between partial actions of an ordered groupoid G on a ring R, in which the domain of each partial bijection is an ideal, and meet-preserving global actions of the Birget–Rhodes expansion GBR of G on R. Using this correspondence, we prove that the partial skew groupoid ring is a homomorphic image of the skew groupoid ring constructed through the Birget–Rhodes expansion.

Actions of Inverse Semigroups on Algebras

In this article we prove that if S is a faithfully projective R-algebra and H is a finite inverse semigroup acting on S as R-linear maps such that the fixed subring S H = R, then any partial isomorphism between ideals of S which are generated by central idempotents can be obtained as restriction of an R-automorphism of S and there exists a finite subgroup of automorphisms G of S with S G = R.

On the separability of the partial skew groupoid ring

Given a partial (resp. a global) action

Representations of the super Jordan plane

\alpha

Lifting partial actions: from groups to groupoids.

α of a connected finite groupoid